The Intertropical Convergence Zone (ITCZ) is a narrow tropical belt of deep convective clouds, intense precipitation, and monsoon circulations encircling the Earth. Complex interactions between the ITCZ and local geophysical dynamics result in high climate variability, making weather forecasting and prediction of extreme rainfall or drought events challenging. We unravel the complex spatio-temporal dynamics of the ITCZ and the resulting teleconnection patterns via a novel tropical climate classification achieved using complex network analysis and community detection. We reduce the high-dimensional complex ITCZ dynamics into a simple yet insightful community structure that classifies the tropics into seven regions representing distinct ITCZ dynamics. The two largest communities, encompassing landmasses over the Northern and Southern hemispheres, are associated with coherent seasonal ITCZ dynamics and have significant long-range connections. Temporal analysis of the community structure highlights that the tropical Pacific and Atlantic Oceans communities exhibit substantial variation on multidecadal scales. Further, these communities exhibit incoherent dynamics due to atmosphere-ocean interactions driven by equatorial and coastal oceanic upwelling.